Manifolds for which the heat kernel is given in terms of geodesic lengths (Q1064641)

The authors give Riemannian manifolds and Lie groups where the heat kernel is given in an exact way by formulas involving only the spectrum of geodesic lengths. The authors discuss compact Lie groups and duals of compact Lie groups and nilpotent Lie groups using this point of view. They also discuss solvable and exponentially solvable Lie groups.